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Parametric-Gain Approach to the Analysis of DPSK Dispersion-Managed Systems

Parametric-Gain Approach to the Analysis of DPSK Dispersion-Managed Systems. Bononi , P. Serena, A. Orlandini, and N. Rossi Dipartimento di Ingegneria dell’Informazione, Università di Parma Viale degli Usberti, 181A, 43100 Parma, Italy e-mail: bononi@tlc.unipr.it. Milan. Parma. Rome.

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Parametric-Gain Approach to the Analysis of DPSK Dispersion-Managed Systems

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  1. Parametric-Gain Approach to the Analysis of DPSK Dispersion-Managed Systems • Bononi, P. Serena, A. Orlandini, and N. Rossi Dipartimento di Ingegneria dell’Informazione, Università di Parma Viale degli Usberti, 181A, 43100 Parma, Italy e-mail: bononi@tlc.unipr.it A. Bononi, China-Italy Workshop Photon. Commun. & Sens.1/21

  2. Milan Parma Rome A. Bononi, China-Italy Workshop Photon. Commun. & Sens.2/21

  3. Outline • Introduction • State of the Art: BER tools in DPSK transmission • The PG Approach: • Key Assumptions • Tools • Results • Conclusions A. Bononi, China-Italy Workshop Photon. Commun. & Sens.3/21

  4. Introduction • Amplified spontaneous emission (ASE) noise from optical amplifiers makes the propagating field intensity time-dependent even in constant-envelope modulation formats such as DPSK. • Random intensity fluctuations, through self-phase modulation (SPM), cause nonlinear phase noise [1], which is the dominant impairment in single-channel DPSK. • Most existing analytical models focus on the statistics of the nonlinear phase noise. [1] J. Gordon et al., Opt. Lett., vol. 15, pp. 1351-1353, Dec. 1990. A. Bononi, China-Italy Workshop Photon. Commun. & Sens.4/21

  5. Tx Matched filter SPM only State of the Art • K.-Po Ho [2] computed the probability density function (PDF) of nonlinear phase noise and derived a BER expression for DPSK systems with optical delay demodulation. Very elegant work, but: • model assumes zero chromatic dispersion (GVD) • does not account for the impact of practical optical/electrical filters on both signal and ASE [2] K.-Po Ho, JOSAB, vol. 20, pp. 1875-1879, Sept. 2003. A. Bononi, China-Italy Workshop Photon. Commun. & Sens.5/21

  6. Tx OBPF LPF no SPM State of the Art • Wang and Kahn [3] computed the exact BER for DPSK (but provided no algorithm details) using Forestieri’s Karhunen-Loeve (KL) method [4] for quadratic receivers in Gaussian noise : • Model accounts for impact of practical optical/electrical filters on both signal and ASE • ....but ignores nonlinearity: it concentrates on GVD only. [3] J. Wang et al., JLT, vol. 22, pp. 362-371, Feb. 2004. [4] E. Forestieri, JLT, vol. 18, pp. 1493-1503, Nov. 2000. A. Bononi, China-Italy Workshop Photon. Commun. & Sens.6/21

  7. N Tx OBPF LPF The PG Approach • Also our group [5] computed the BER for DPSK using Forestieri’s KL method. Our model: • besides accounting for impact of practical optical/electrical filters • also accounts for the interplay of GVD and nonlinearity, including the signal-ASE nonlinear interaction using the tools developed in the study of parametric gain (PG) • is tailored to dispersion-managed (DM) long-haul systems [5] P. Serena et al., JLT, vol. 24, pp. 2026-2037, May 2006. A. Bononi, China-Italy Workshop Photon. Commun. & Sens.7/21

  8. DPSK RX N in-line Tx LPF OBPF post pre Dispersion Map D A DPSK DM System KL method requires Gaussian field statistics at receiver (RX), after optical filter A. Bononi, China-Italy Workshop Photon. Commun. & Sens.8/21

  9. D= ps/nm/km in-line Din =0 Why Gaussian Field? • At zero dispersion, PDF of ASE RX field before OBPF is strongly non-Gaussian [2] …but with some dispersion, PDF contours become elliptical  Gaussian PDF Im[E] Im[E] 3 4 2 0 1 D Re[E] Re[E] Single span OSNR= 25 dB/0.1nm FNL = 0.15p rad [2] K.-Po Ho, JOSAB, vol. 20, pp. 1875-1879, Sept. 2003. A. Bononi, China-Italy Workshop Photon. Commun. & Sens.9/21

  10. Iafter OBPF, Bo=10 GHz [6] A. Orlandini et al., ECOC’06, Sept. 2006. Why Gaussian Field? • Even at zero dispersion... PDF of ASE RX field AFTER OBPF Gaussianizes [6] before OBPF Red: Monte Carlo (MC) Blue: Multicanonical MC (MMC) OSNR=10.8 dB/0.1 nm, FNL=0.2p, ASE BW BM=80 GHz A. Bononi, China-Italy Workshop Photon. Commun. & Sens.10/21

  11. If optical filter bandwidth Bo << BM, n(t) is the sum of many comparable-size independent samples Central Limit Theorem Gaussian whatever the input noise distribution Why Gaussian Field? Reason is that a white ASE over band BM remains white after SPM h(t) w(t) n(t) OBPF SPM A. Bononi, China-Italy Workshop Photon. Commun. & Sens.11/21

  12. Having shown the plausibility of the Gaussian assumption for the RX field, it is now enough to evaluate its power spectral density (PSD) to get all the needed information, to be passed to the KL BER routine. • A linearization of the dispersion-managed nonlinear Schroedinger equation (DM-NLSE) around the signal provides the desired PSDs, according to the theory of parametric gain. A. Bononi, China-Italy Workshop Photon. Commun. & Sens.12/21

  13. Rx ASE is Gaussian Small perturbation Linear PG Model [7] C. Lorattanasane et al., JQE, July 1997 [8] A. Carena et al., PTL, Apr. 1997 [9] M. Midrio et al., JOSA B, Nov. 1998 [5] P. Serena et al., JLT, vol. 24, pp. 2026-2037, May 2006. DM, finite N spans DM, infinite spans A. Bononi, China-Italy Workshop Photon. Commun. & Sens.13/21

  14. No pre-, post-comp. Red : quadrature ASE » Blue: in-phase ASE Parametric Gain = Gain (dB) over white-ASE case due to Parametric interaction signal-ASE Linear PG Model A. Bononi, China-Italy Workshop Photon. Commun. & Sens.14/21

  15. Limits of Linear PG Model • linear PG model (dashed) versus Monte-Carlo BPM simulation (solid) FNL=0.55 p rad, D=8 ps/nm/km, Din=0 /0.1 nm /0.1 nm A. Bononi, China-Italy Workshop Photon. Commun. & Sens.15/21

  16. @ PG doubling strengths for 10 Gb/s NRZ end-line OSNR (dB/0.1nm) DM systems with Din=0. ( N>>1 spans) 1.4 21 1.2 19 17 1 ] p 15 15 0.8 [rad/ For fixed OSNR (e.g. 15dB) in region well below red PG-doubling curve: • Linear PG model holds • ASE ~ Gaussian NL F 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Map strength S ( DR2 ) [10] P.Serena et al., JLT, vol. 23, pp. 2352-2363, Aug. 2005. A. Bononi, China-Italy Workshop Photon. Commun. & Sens.16/21

  17. Our BER Algorithm Steps of our semi-analytical BER evaluation algorithm: • Rx DPSK signal obtained by noiseless BPM propagation (includes ISI from DM line) • ASE at RX assumed Gaussian. PSD obtained either from linear PG model (small FNL) or estimated off-line from Monte-Carlo BPM simulations (large FNL). Reference FNL for PSD computation suitably decreased from peak value to average value for increasing transmission fiber dispersion (map strength). • Data from steps 1, 2 passed to Forestieri’s KL BER evaluation algorithm, suitably adapted to DPSK. A. Bononi, China-Italy Workshop Photon. Commun. & Sens.17/21

  18. NRZ RZ-33% Theory Exp. Results • Check with experimental results [H. Kim et al., PTL, Feb. ’03] 10 Gb/s single-channel system, 6100 km NZDSF A. Bononi, China-Italy Workshop Photon. Commun. & Sens.18/21

  19. NRZ-DPSK NRZ-OOK RZ-DPSK 50% Results R=10 Gb/s single-channel, 20100 km, D=8 ps/nm/km, Din=0. OSNR=11 dB/0.1 nm, Bo=1.8R Noiseless optimized Dpre, Dpost 1E-9 BER 1E-4 1E-2 A. Bononi, China-Italy Workshop Photon. Commun. & Sens.19/21

  20. Results 10 Gb/s single-channel system, 20100 km, Din=0. Bo=1.8R . Noiseless optimized Dpre, Dpost. DPSK-NRZ DPSK-RZ (50%) @ D=8 ps/nm/km PG no PG ΦNL=0.5 ΦNL=0.5 ΦNL=0.3 ΦNL=0.1 ΦNL=0.3 Strength ( DR2) Strength ( DR2) A. Bononi, China-Italy Workshop Photon. Commun. & Sens.20/21

  21. More information on our work: www.tlc.unipr.it Conclusions • Novel semi-analytical method for BER estimation in DPSK DM optical systems. • The striking difference between OOK and DPSK is that in DPSK PG impairs the system at much lower nonlinear phases, when the linear PG model still holds. Hence for penalties up to ~3 dB one can use the analytic ASE PSDs from the linear PG model instead of the time-consuming off-line MC PSD estimation. • Hence our mehod provides a fast and effective tool in the optimization of maps for DPSK DM systems. A. Bononi, China-Italy Workshop Photon. Commun. & Sens.21/21

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